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  GR9277 #52
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A particle of mass m is confined to an infinitely deep square-well potential:
<br />
 V(x)&=&\infty,\;\;x\leq0,x\geq a \\<br />
 V(x)&=&0,\;\;0\lt x \lt a<br />

The normalized eigenfunctions, labeled by the quantum number n, are $\psi_n=\sqrt{\frac{2}{a}}\sin \frac{n\pi x}{a}$

The eigenfunctions satisfy the condition $\int_0^a \psi_n^*(x)\psi_l(x)dx=\delta_{nl},\delta_{nl}=1$ if $n=l$, otherwise $\delta_{nl}=0$. This is a statement that the eigenfunctions are

  1. solutions to the Schrodinger equation
  2. orthonormal
  3. bounded
  4. linearly dependent
  5. symmetric

Quantum Mechanics}Orthonormality

\langle \psi_m | \psi_n \rangle = \delta_{nm}

This is the definition of orthonormality, i.e., something that is both orthogonal (self dot others = 0) and normal (self dot self = 1).

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2009-07-13 22:25:51
So, the answer is (B).NEC

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